Method and system for point-to-point fast delay estimation for VLSI circuits

ABSTRACT

The present disclosure is directed to a method for estimating an interconnect delay for a source-to-sink path of a net within a Very Large Scale Integration (VLSI) circuit, the source-to-sink path connecting a source and a sink in the net. The method may comprise estimating a total wire capacitance; calculating a delay contribution based on delay of the source-to-sink path and delay of a plurality of off-path sinks; and estimating the interconnect delay for the source-to-sink path based on the delay contribution.

TECHNICAL FIELD

The present disclosure generally relates to a method of estimatinginterconnect delay in an integrated circuit design, and moreparticularly to a method for estimating interconnect delay in a VeryLarge Scale Integration (VLSI) circuit.

BACKGROUND

Interconnect delay has moved to the forefront as the limiting factor inintegrated circuit performance. The recognition of interconnect delay isincreasingly important as advancements in deep-submicron processgeometries allow companies to build smaller, faster and less-expensivetransistors. By way of example, interconnect delay may account for morethan 75 percent of total path delay in a Very Large Scale Integration(VLSI) circuit. Interconnect delay is the time delay from selected inputto selected output points along a given interconnect. Interconnect delaydemonstrates a degree of resistance, capacitance, and to a considerablylesser degree, inductance. While the impedance might be almostnegligible in a single interconnect, even an extremely small value mayhave a significant effect on the maximum response speed of the circuit.The delay caused by possibly millions of such interconnects in a VLSIcircuit may have a profound effect on reducing the maximum operatingefficiencies of the integrated circuit.

SUMMARY

Accordingly, an embodiment of the present disclosure is directed to amethod for estimating an interconnect delay for a source-to-sink path ofa net within a Very Large Scale Integration (VLSI) circuit, thesource-to-sink path connecting a source and a sink in the net. Themethod may comprise calculating an off-path-point that represents allother off-path sinks in the net; projecting an intersect from theoff-path-point to the source-to-sink path; estimating a total wirecapacitance; calculating a delay contribution based on delay of thesource-to-sink path and delay of said all other off-path sinks; andestimating the interconnect delay for the source-to-sink path based onthe delay contribution.

A further embodiment of the present disclosure is directed to a methodfor estimating an interconnect delay for a source-to-sink path of a netwithin a Very Large Scale Integration (VLSI) circuit, the source-to-sinkpath connecting a source and a sink in the net. The method may compriseprojecting a plurality of off-path sinks to the source-to-sink path;estimating a total wire capacitance; calculating an individual delaycontribution for each one of the plurality of off-path sinks;calculating a delay contribution based on delay of the source-to-sinkpath and delay of the plurality of off-path sinks; and estimating theinterconnect delay for the source-to-sink path based on the delaycontribution.

A further embodiment of the present disclosure is directed to acomputer-readable medium having computer-executable instructions forperforming a method for estimating an interconnect delay for asource-to-sink path of a net within a Very Large Scale Integration(VLSI) circuit, the source-to-sink path connecting a source and a sinkin the net. The computer-executable instructions for performing themethod may comprise estimating a total wire capacitance; calculating adelay contribution based on delay of the source-to-sink path and delayof a plurality of off-path sinks; and estimating the interconnect delayfor the source-to-sink path based on the delay contribution.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary only and are notnecessarily restrictive of the disclosure as claimed. The accompanyingdrawings, which are incorporated in and constitute a part of thespecification, illustrate an embodiment of the disclosure and togetherwith the general description, serve to explain the principles of thedisclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The numerous advantages of the present disclosure may be betterunderstood by those skilled in the art by reference to the accompanyingfigures in which:

FIG. 1 is a flow diagram illustrating a method for estimating aninterconnect delay for an integrated circuit;

FIG. 2 is an illustration depicting a connection between a specificsource and a specific sink among all sinks in a net in an exemplary VLSIcircuit;

FIG. 3 is another flow diagram illustrating a method for estimating aninterconnect delay for an integrated circuit;

FIG. 4 is another illustration depicting a connection between a sourceand a sink in an exemplary VLSI circuit; and

FIG. 5 is a block diagram illustrating a system for estimating aninterconnect delay for an integrated circuit.

DETAILED DESCRIPTION

Reference will now be made in detail to the subject matter disclosed,which is illustrated in the accompanying drawings.

When designing a new chip or implementing its manufacture, it isoftentimes desirable to determine a maximum clock frequency at which thechip will operate. In order to determine this maximum clock frequency,an interconnect delay effect (among other things) must be predicted.Several methods have been employed by circuit designers to effectivelypredict the effect of interconnect delay. Because an exact solution ofthe time delays in interconnects may require the solution to a set ofcomplex differential equations, circuit designers sometimes rely uponsimplifications and modeling to come up with timing estimates. Onecommonly used model represents interconnects as resistors andcapacitances in series and parallel. This model produces an RC(Resistance-Capacitance) tree.

An RC tree, or any net topology tree, may be constructed from a designmodel: a directed graph representing the “netlist” of the logic design,where each pin in an Integrated Circuit (IC) is associated with a“cell”. A net may be understood as a set of interconnect segments thattransfer the same logic signal from a source to all sinks of the net.Each cell has an associated location, e.g., x,y coordinates of the cellin the IC. Also associated with each cell may be physical informationproviding cell dimensions and pin offsets relative to the cell origin.The cell location and pin offsets may be combined to determine thelocations of each source and sink pin on a net. A net topology tree maythen be constructed from this data. The tree may be estimated utilizing,for example, a minimum Steiner tree. Alternatively, an actual orpreferred wire route produced by a routing tool may be used. Once a treehas been constructed, an interconnect delay estimator may then use thetree to perform its calculations.

In VLSI physical designs (including floorplan and placement of thedesigns), one may need to estimate delay of one specific source-to-sinkpath (e.g., between a specific source to a specific sink) multiple timesin order to make optimization decisions. The aforementioned methods maybe time consuming for providing such estimations. Therefore, a methodfor providing point-to-point interconnect delay estimation in a VLSIcircuit may be appreciated.

Referring now to FIGS. 1 and 2. FIG. 1 shows a flow diagram illustratingsteps performed by one embodiment of a method 100 in accordance with thepresent disclosure. The method may be configured for providing accurateand timely interconnect delay estimation in a Very Large ScaleIntegration (VLSI) circuit. FIG. 2 depicts a connection between a source(S₀) and a sink (S_(i)) in an exemplary VLSI circuit. The method 100 maybe utilized for estimating an interconnect delay between the source (S₀)and the sink (S_(i)) in the VLSI circuit.

For instance, a source-to-sink path 202 of a net of a VLSI circuit maybe given/specified. The given source-to-sink path 202 connects a source(S₀) and a sink (S_(i)) in the net of the VLSI circuit. It is understoodthat the source, the sink, and the path 202 depicted in FIG. 2 aremerely exemplary; different sources, sinks, and/or paths may beselected/identified for estimation without departing from the scope andspirit of the present disclosure.

In one embodiment, method 100 moves to an operation 110 after a startoperation. Operation 110 may calculate an off-path-point (S_(other))that may represent all other off-path sinks in the net of the VLSIcircuit. Off-path sinks are all other sinks in the same net that are noton the source-to-sink path 202. In one embodiment, the off-path-point(S_(other)) may be calculated as a weighted center of gravity (COG) ofall other sinks. The sinks may be uniformly weighted or capacitanceweighted for the COG calculation.

Operation 120 may obtain an intersect by projecting the off-path-pointto the source-to-sink path. In one embodiment, the intersect may beobtained by finding a bounding box defined by the source (S₀) and thesink (S_(i)), and then find a point on the bounding box that is closestto the off-path-point (S_(other)). For example, as illustrated in FIG.2, the intersect is obtained as the closest point 204 from thesource-to-sink path 202 (a part of the bounding box) to the COG of theall other sinks (S_(other)).

Operation 130 may estimate a total wire capacitance c(T). In oneembodiment, the total wire capacitance c(T) may be estimated asc(T)=C₀×Total Wire Length, where C₀ is the unit wire capacitance (i.e.,wire capacitance per unit length), and the Total Wire Length may beestimated utilizing a geometric look-up table as presented by Chu,FLUTE: Fast Lookup Table Based Wirelength Estimation Technique, IEEEInternational Conference on Computer Aided Design, pages 696-701,November 2004, which is hereby incorporated by reference in itsentirety. The geometric look-up table may be utilized directly if thenumber of pins on the VLSI circuit is less than or equal to 9;otherwise, the sinks may be divided into smaller groups for the look-uptable to apply.

Alternatively, the total wire length (TWL) may be estimated based on theformula:TWL=k√{square root over (n·w_(R) ·h _(R))}where

n is the number of pins on the VLSI circuit;

$w_{R} = {{width} \cdot \frac{n + 1}{n - 1}}$where width is the width of the VLSI circuit;

$h_{R} = {{height} \cdot \frac{n + 1}{n - 1}}$where height is the height of the VLSI circuit; and

k is the ratio

$\frac{{cost}({RMST})}{\sqrt{{area} \cdot n}}$as presented by Caldwell et al., On Wirelength Estimations for Row-basedPlacement, IEEE Transactions on Computer-Aided Design of IntegratedCircuits and Systems, vol. 18, pages 1265-1278, September 1999, which ishereby incorporated by reference in its entirety. As presented byCaldwell et al., the value of k may be obtained from a lookup tablebased on value of n and aspect ratio

${AR} = {{\max\left( {\frac{w_{R}}{h_{R}},\frac{h_{R}}{w_{R}}} \right)}.}$

It is contemplated that the total wire length (TWL) may be estimatedbased on half-perimeter (i.e., w_(R)+h_(R)) instead of area (i.e.,w_(R)·h_(R)) if the number of pins is less than four (i.e.,TWL=k·√{square root over (n·(w_(R)+h_(R)))} where n<4). It is understoodthat the aforementioned formulas are merely one method for estimatingthe total wire length. Therefore, it is also contemplated that othermethods/techniques for estimating the total wire length may be utilizedwithout departing from the scope and spirit of the present disclosure.

Operation 140 may calculate a delay contribution due to the path 202 anddelays caused by the off-path sinks. The delay contribution may becalculated by finding a wire resistance, then utilizing total wirecapacitance minus source-sink capacitance to find a wire loadcapacitance and total capacitances of other sinks. For example, in oneembodiment, the delay from the source (S₀) to the sink (S_(i)) may becalculated based on the formula:

${{Delay}\left( {S_{0},S_{i}} \right)} = {{0.5 \cdot R_{0} \cdot C_{0} \cdot \left( {{distance}\left( {S_{0},S_{i}} \right)} \right)^{2}} + {R_{0} \cdot {{distance}\left( {S_{0},S_{i}} \right)} \cdot {c\left( S_{i} \right)}} + {{R_{0} \cdot {project\_ distance}}{\left( {S_{0},S_{other},S_{i}} \right) \cdot \left( {{c(T)} - {C_{0} \cdot {{distance}\left( {S_{0},S_{i}} \right)}} + {\sum\limits_{{j = {{1\ldots\; i} - 1}},{i + {1\ldots\; n} - 1}}{c\left( S_{j} \right)}}} \right)}}}$where

-   -   R₀ is the unit wire resistance (i.e., wire resistance per unit        length);    -   C₀ is the unit wire capacitance (i.e., wire capacitance per unit        length);    -   c(S_(i)) represents the loading capacitance of the sink S_(i);    -   c(T) is the total wire capacitance estimated based on formula    -   c(T)=C₀×Total Wire Length as previously described;

$\sum\limits_{{j = {{1\ldots\; i} - 1}},{i + {1\ldots\; n} - 1}}{c\left( S_{j} \right)}$represents the sum of all other sinks' loading capacitance;

-   -   distance(S₀, S_(i)) represents the measurable distance between        the source S₀ and the sink S_(i); and    -   project_distance(S₀,S_(other),S_(i)) represents the distance        from the source S₀ to the intersect 204 projected on to the path        202 (this distance is bounded by distance(S₀, S_(i))).

Operation 150 may compute a delay due to gate output resistance (may bereferred to as gate delay) for the VLSI circuit. For example, the gatedelay may be computed utilizing conventional techniques/methods (e.g.,K-factor model or Lumped C method) based on the sum of the total wirecapacitance c(T) and all sink capacitances. For instance, the gate delaymay be computed as gate delay=gate output resistance×(c(T)+sum ofcapacitance of all sinks). It is contemplated that the effectivecapacitance concept may be applied in the gate delay computation aswell.

Operation 160 may estimate the interconnect delay between the source S₀and the sink S_(i). For example, if the only focus is on the wire, thenthe gate delay may be ignored, and the interconnect delay between thesource and the sink may be substantially equal to the sum of delaycaused by off-path sinks and delay due to direct connection from sourceto the specific sink (i.e., estimated interconnect delay equals Delay(S₀,S_(i)) as calculated in operation 140). In another example, theinterconnect delay may be estimated as the sum of Delay(S₀,S_(i)) andthe delay due to gate output resistance (i.e., estimated interconnectdelay equals Delay(S₀,S_(i))+gate delay). It is understood that themethod may be applied to provide estimates for other connectionsconnecting different sources and/or sinks.

Referring to FIG. 3, a flow diagram illustrating steps performed by analternative embodiment of method 300 in accordance with the presentdisclosure is shown. FIG. 4 depicts a connection between a source (S₀)and a sink (S_(i)) in an exemplary VLSI circuit. The method 300 may beutilized for estimating an interconnect delay between the source (S₀)and the sink (S_(i)) in the VLSI circuit.

In this embodiment, method 300 moves to an operation 310 after a startoperation. Based on the source-to-sink path given/specified, operationsmay be carried out to determine a delay contributed by all otheroff-path sinks without calculating an off-path-point (S_(other)). Forexample, operation 310 may project each off-path sink to a point on thesource-to-sink path. In this example, as illustrated in FIG. 4, insteadof finding a COG point representing all off-patch sinks, an off-pathsink S₁, S₂ . . . S_(k) may be directly projected on to the path.

Operation 130 may estimate a total wire capacitance c(T), and operation320 may calculate an individual delay contributed by each off-path sinkbased on the projection of this particular off-path sink (e.g.,utilizing conventional methods/techniques for delay calculation based onthe projected points). Operation 340 may then calculate a total delaycontributed by all off-path sinks (e.g., the total delay contributed maybe calculated as a sum of all individual delay contributions).

Method 300 may comprise operation 150 for computing a delay due to gateoutput resistance (may be referred to as gate delay) for the VLSIcircuit. In addition, operation 160 may estimate the interconnect delaybetween the source S₀ and the sink S_(i). For example, if the only focusis on the wire, then the gate delay may be ignored, and the interconnectdelay between the source and the sink may substantially equal to thedelay caused by off-path sinks (i.e., the delay calculated in operation340). In another example, the interconnect delay may be estimated as thesum of the delay contribution and the gate delay (i.e.,Delay(S₀,S_(i))+gate delay).

It is contemplated that additional alternative embodiment of the methodmay be utilized for estimating an interconnect delay for asource-to-sink path. For example, the set of all off-path sinks may bedivided into multiple subsets based on their location on the circuitry.Each subset may calculate its own off-path-point (e.g., COG of thesubset) to represent that particular subset. These off-path-points maybe projected to the source-to-sink path and utilized for estimating theinterconnect delay.

Referring to FIG. 5, a block diagram illustrating a system 500 forestimating an interconnect delay for an integrated circuit is shown. Thesystem 500 may comprise a wire length estimating module 502 configuredfor estimating a total wire length. A computing/calculating module 504may be configured for performing various computations. Such computationsmay include, for example, calculating an off-path-point (S_(other)),calculating a delay contribution caused by all off-path sinks, computinga gate delay for the VLSI circuit, and/or calculating an individualdelay contributed by each off-path sink. A delay estimating module 506may be configured for estimating the interconnect delay based on thedelay contribution and optionally the gate delay (based on estimationrequirements).

In the present disclosure, the methods disclosed may be implemented assets of instructions or software readable by a device. Further, it isunderstood that the specific order or hierarchy of steps in the methodsdisclosed are examples of exemplary approaches. Based upon designpreferences, it is understood that the specific order or hierarchy ofsteps in the method can be rearranged while remaining within thedisclosed subject matter. The accompanying method claims presentelements of the various steps in a sample order, and are not necessarilymeant to be limited to the specific order or hierarchy presented.

It is believed that the present disclosure and many of its attendantadvantages will be understood by the foregoing description, and it willbe apparent that various changes may be made in the form, constructionand arrangement of the components without departing from the disclosedsubject matter or without sacrificing all of its material advantages.The form described is merely explanatory, and it is the intention of thefollowing claims to encompass and include such changes.

1. A method, performed by a processor executing non-transitory computerusable program code, for estimating an interconnect delay for asource-to-sink path of a net within a Very Large Scale Integration(VLSI) circuit, the source-to-sink path connecting a source and a sinkin the net, comprising: calculating by the processer an off-path-pointthat represents all other off-path sinks in the net; projecting anintersect from the off-path-point to the source-to-sink path; estimatinga total wire capacitance; calculating a delay contribution based ondelay of the source-to-sink path and delay of said all other off-pathsinks; and estimating the interconnect delay for the source-to-sink pathbased on the delay, wherein calculating a delay contribution based ondelay of the source-to-sink path and delay of said art other off-pathsinks comprises: calculating the delay contribution according to theformula${{Delay}\left( {S_{0},S_{i}} \right)} = {{0.5 \cdot R_{0} \cdot C_{0} \cdot \left( {{distance}\left( {S_{0},S_{i}} \right)} \right)^{2}} + {R_{0} \cdot {{distance}\left( {S_{0},S_{i}} \right)} \cdot {c\left( S_{i} \right)}} + {{R_{0} \cdot {project\_ distance}}{\left( {S_{0},S_{other},S_{i}} \right) \cdot {\left( {{c(T)} - {C_{0} \cdot {{distance}\left( {S_{0},S_{i}} \right)}} + {\sum\limits_{{j = {{1\ldots\; i} - 1}},{i + {1\ldots\; n} - 1}}{c\left( S_{j} \right)}}} \right).}}}}$2. The method as claimed in claim 1, further comprising: computing adelay due to gate output resistance for the VLSI circuit; and refiningthe estimated interconnect delay for the source-to-sink path based onthe delay contribution and the delay due to gate output resistance. 3.The method as claimed in claim 1, wherein calculating an off-path-pointthat represents all other off-path sinks in the net comprises: computinga center of gravity of all other sinks.
 4. The method as claimed inclaim 1, wherein calculating an off-path-point that represents all otheroff-path sinks in the net comprises: calculating a weighted center ofgravity utilizing at least one of uniform weighting of all other sinksor capacitance weighting of all other sinks.
 5. The method as claimed inclaim 1, wherein estimating a total wire capacitance comprises:estimating the total wire capacitance according to formulac(T)=C ₀×Total Wire Length.
 6. The method as claimed in claim 5, whereinthe total wire length is estimated according to formula${TWL} = \left\{ \begin{matrix}{{{k \cdot \sqrt{n \cdot w_{R} \cdot h_{R}}}\mspace{14mu}{when}\mspace{14mu} n} \geq 4} \\{{{k \cdot \sqrt{n \cdot \left( {w_{R} \cdot h_{R}} \right)}}\mspace{14mu}{when}\mspace{14mu} n} < 4.}\end{matrix} \right.$
 7. A method, performed by a processor executingnon-transitory computer usable program code, for estimating aninterconnect delay for a source-to-sink path of a net within a VeryLarge Scale Integration (VLSI) circuit, the source-to-sink pathconnecting a source and a sink in the net, comprising: projecting aplurality of off-path sinks to the source-to-sink path; estimating atotal wire capacitance; calculating by the processer an individual delaycontribution for each one of the plurality of off-path sinks;calculating a delay contribution based on delay of the source-to-sinkpath and delay of the plurality of off-path sinks; estimating theinterconnect delay for the source-to-sink path based on the delay,wherein calculating a delay contribution based on delay of thesource-to-sink path and delay of said art other off-path sinkscomprises: calculating the delay contribution according to the formula${{Delay}\left( {S_{0},S_{i}} \right)} = {{0.5 \cdot R_{0} \cdot C_{0} \cdot \left( {{distance}\left( {S_{0},S_{i}} \right)} \right)^{2}} + {R_{0} \cdot {{distance}\left( {S_{0},S_{i}} \right)} \cdot {c\left( S_{i} \right)}} + {{R_{0} \cdot {project\_ distance}}{\left( {S_{0},S_{other},S_{i}} \right) \cdot {\left( {{c(T)} - {C_{0} \cdot {{distance}\left( {S_{0},S_{i}} \right)}} + {\sum\limits_{{j = {{1\ldots\; i} - 1}},{i + {1\ldots\; n} - 1}}{c\left( S_{j} \right)}}} \right).}}}}$8. The method as claimed in claim 7, further comprising: computing adelay due to gate output resistance for the VLSI circuit; and refiningthe estimated interconnect delay for the source-to-sink path based onthe delay contribution and the delay due to gate output resistance. 9.The method as claimed in claim 8, wherein estimating a total wirecapacitance comprises: estimating the total wire capacitance accordingto formulac(T)=C ₀×Total Wire Length.
 10. The method as claimed in claim 9,wherein the total wire length is estimated according to formula${TWL} = \left\{ \begin{matrix}{{{k \cdot \sqrt{n \cdot w_{R} \cdot h_{R}}}\mspace{14mu}{when}\mspace{14mu} n} \geq 4} \\{{{k \cdot \sqrt{n \cdot \left( {w_{R} \cdot h_{R}} \right)}}\mspace{14mu}{when}\mspace{14mu} n} < 4.}\end{matrix} \right.$
 11. A non-transitory computer-readable mediumhaving computer-executable instructions for performing a method forestimating an interconnect delay for a source-to-sink path of a netwithin a Very Large Scale Integration (VLSI) circuit, the source-to-sinkpath connecting a source and a sink in the net, comprising: estimating atotal wire capacitance; calculating a delay contribution based on delayof the source-to-sink path and delay of a plurality of off-path sinks;and estimating the interconnect delay for the source-to-sink path basedon the delay, wherein calculating a delay contribution based on delay ofthe source-to-sink path and delay of a plurality of off-path sinkscomprises: calculating the delay contribution according to formula${{Delay}\left( {S_{0},S_{i}} \right)} = {0.5 - {R_{0} \cdot C_{0} \cdot \left( {{distances}\left( {S_{0},S_{i}} \right)} \right)^{2}} + {R_{0} \cdot {{distance}\left( {S_{0},S_{i}} \right)} \cdot {c\left( S_{i} \right)}} + {{R_{0} \cdot {project\_ distance}}{\left( {S_{0},S_{other},S_{i}} \right) \cdot {\left( {{c(T)} - {C_{0} \cdot {{distance}\left( {S_{0},S_{i}} \right)}} + {\sum\limits_{{j = {{1\ldots\; i} - 1}},{i + {1\ldots\; n} - 1}}{c\left( S_{j} \right)}}} \right).}}}}$12. The method as claimed in claim 11, further comprising: computing adelay due to gate output resistance for the VLSI circuit; and refiningthe estimated interconnect delay for the source-to-sink path based onthe delay contribution and the delay due to gate output resistance. 13.The method as claimed in claim 11, wherein estimating a total wirecapacitance comprises: estimating the total wire capacitance accordingto formulac(T)=C ₀×Total Wire Length.
 14. The method as claimed in claim 13,wherein the total wire length is estimated according to formula${TWL} = \left\{ \begin{matrix}{{{k \cdot \sqrt{n \cdot w_{R} \cdot h_{R}}}\mspace{14mu}{when}\mspace{14mu} n} \geq 4} \\{{{k \cdot \sqrt{n \cdot \left( {w_{R} \cdot h_{R}} \right)}}\mspace{14mu}{when}\mspace{14mu} n} < 4.}\end{matrix} \right.$
 15. The non-transitory computer-readable mediumhaving computer-executable instructions for performing a method asclaimed in claim 11, wherein calculating a delay contribution based ondelay of the source-to-sink path and delay of a plurality of off-pathsinks comprises: calculating an off-path-point that represents all otheroff-path sinks in the net; projecting an intersect from theoff-path-point to the source-to-sink path; and calculating a delaycontribution based on delay of the source-to-sink path and delay of allother off-path sinks.
 16. The method as claimed in claim 15, whereincalculating an off-path-point that represents all other off-path sinksin the net comprises: computing a center of gravity of all other sinks.17. The method as claimed in claim 15, wherein calculating anoff-path-point that represents all other off-path sinks in the netcomprises: calculating a weighted center of gravity utilizing at leastone of uniform weighting of all other sinks or capacitance weighting ofall other sinks.
 18. The computer-readable medium havingcomputer-executable instructions for performing a method as claimed inclaim 11, wherein calculating a delay contribution based on delay of thesource-to-sink path and delay of a plurality of off-path sinkscomprises: projecting the plurality of off-path sinks to thesource-to-sink path; calculating an individual delay contribution foreach one of the plurality of off-path sinks; and calculating a delaycontribution based on delay of the source-to-sink path and delay of theplurality of off-path sinks based on the individual delay contributionfor each one of the plurality of off-path sinks.